Tuesday, August 12, 2014

Safe library - generalising functions

Summary: The Safe library now has exact versions of take/drop, with twelve functions implemented on top of a generalised splitAt.

The Safe library is a simple Haskell library that provides versions of standard Prelude and Data.List functions that usually throw errors (e.g. tail), but wrapped to provide better error messages (e.g. tailNote), default values (e.g. tailDef) and Maybe results (e.g. tailMay).

I recently released version 0.3.5, which provides a new module Safe.Exact containing crashing versions of functions such as zip/zipWith (which error if the lists are not equal length) and take/drop/splitAt (which error if there are not enough elements), then wraps them to provide safe variants. As an example, the library provides:

takeExact    :: Int -> [a] -> [a]
takeExactMay :: Int -> [a] -> Maybe [a]

These are like take, but if the Int is larger than the length of the list it will throw an error or return Nothing. Some sample evaluations:

takeExactMay 2 [1,2,3] == Just [1,2]
takeExact    2 [1,2,3] == [1,2]
takeExactMay 2 [1] == Nothing
takeExact    2 [1] ==
    1:error "Safe.Exact.takeExact, index too large, index=2, length=1"
take 1 (takeExact 2 [1]) == [1]

So takeExactMay computes up-front whether the whole computation will succeed, and returns a Nothing if it will fail. In contrast, takeExact produces elements while they are present, but if you demand an additional element that is missing it will result in an error. All the exceptions in the Safe library are designed to provide the maximum level of detail about what went wrong, here telling us the index we were after and the length of the list.

The library provides takeExact, dropExact and splitAtExact, plus Def/May/Note versions, resulting in twelve similar functions. While the implementation of any one function is reasonably short (although not that short, once proper error messages are provided), I didn't want to write the same code twelve times. However, generalising over functions that check up-front and those that check on-demand requires a bit of thought. In the end I settled for:

splitAtExact_ :: (String -> r) -> ([a] -> r) -> (a -> r -> r) -> Int -> [a] -> r
splitAtExact_ err nil cons o xs
    | o < 0 = err $ "index must not be negative, index=" ++ show o
    | otherwise = f o xs
        f 0 xs = nil xs
        f i (x:xs) = x `cons` f (i-1) xs
        f i [] = err $
            "index too large, index=" ++ show o ++ ", length=" ++ show (o-i)

Here the splitAtExact_ function has a parameterised return type r, along with three functional arguments that construct and consume the r values. The functional arguments are:

  • err :: String -> r, says how to convert an error into a result value. For up-front checks this produces a Nothing, for on-demand checks this calls error.
  • nil :: [a] -> r, says what to do once we have consumed the full number of elements. For take we discard all the remaining elements, for drop we are only interested in the remaining elements.
  • cons :: a -> r -> r, says how to deal with one element before we reach the index. For take this will be (:), but for functions producing a Maybe we have to check the r parameter first.

With this generalisation, I was able to write all twelve variants. As a few examples:

addNote fun msg = error $ "Safe.Exact." ++ fun ++ ", " ++ msg

takeExact = splitAtExact_ (addNote "takeExact") (const []) (:)

dropExact = splitAtExact_ (addNote "dropExact") id (flip const)

takeExactMay = splitAtExact_ (const Nothing) (const $ Just []) (\a -> fmap (a:))

dropExactMay = splitAtExact_ (const Nothing) Just (flip const)

splitAtExact = splitAtExact_ (addNote "splitAtExact")
    (\x -> ([], x)) (\a b -> first (a:) b)

splitAtExactMay = splitAtExact_ (const Nothing)
    (\x -> Just ([], x)) (\a b -> fmap (first (a:)) b)

Normally I would have defined takeExact and dropExact in terms of fst/snd on top of splitAtExact. However, in the Safe library error messages are of paramount importance, so I go to additional effort to ensure the error says takeExact and not splitAtExact.

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